6 Key excerpts on "Conservation Laws"

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  eBook - ePub

  The Quantum World

  Quantum Physics for Everyone

  • Kenneth W. Ford(Author)
  • 2005(Publication Date)
  • Harvard University Press

    (Publisher)

  This is no surprise, for everything in the large-scale world is built ultimately of subatomic units. So you can think of the causal link going from small to large: energy, momentum, angular momentum, and charge are conserved in the large-scale world because they are conserved in the subatomic world. The Conservation Laws that govern these quantities are regarded as absolute. An absolute conservation law is one for which no confirmed violation has ever been seen and which is believed to be valid under all circumstances. Moreover, we have theoretical reason to believe that these four laws are absolute. Relativity and quantum theory join to predict that these laws should be valid. But experiment is the final arbiter. No amount of beautiful theory trumps experiment. Calling these Conservation Laws absolute must be as tentative as every other firm pronouncement about nature. Energy In Chapter 6, I introduced the “downhill rule” for quantum jumps. A spontaneous transition must be from a higher to a lower-energy state. A particle can decay only into particles whose total mass is less than the mass of the decaying particle. And, as described earlier in this chapter, energy conservation also plays an essential role in “uphill” events such as the creation of new particles in a proton-proton collision. There is such abundant evidence that the energy after a reaction is the same as the energy before that the law of energy conservation becomes a practical tool for analyzing the complex debris created in particle collision. Momentum Momentum conservation is so well established that it, like energy conservation, becomes a tool of analysis in particle processes. With the help of these laws, physicists can work backward to deduce the masses of new particles that are created. One of the prohibitions resulting from the joint workings of energy conservation and momentum conservation is the prevention of one-particle decays

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  The Biggest Ideas in the Universe 1

  Space, Time and Motion

  • Sean Carroll(Author)
  • 2022(Publication Date)
  • Oneworld Publications

    (Publisher)

  An object can have energy because it is moving, because it’s located at a high elevation, because it’s hot, because it’s massive, because it’s electrically charged, or for other reasons. Under the right circumstances, those forms of energy can be converted back and forth between each other. The energy that a wineglass has just from being located on a table can, if the glass is knocked off the edge, rapidly be converted into energy of motion as it falls, and then into heat and noise and other forms of dissipated energy as it breaks on the floor. Conservation of energy is simply the idea that the total energy, given by adding up all the individual forms, remains constant throughout the whole process.

  (Wait—is this circular reasoning? Are we merely inventing a bunch of quantities that add up to a constant number by definition, calling that “energy,” and congratulating ourselves for discovering a law of physics? No. There is an independent way to define energy and then show that it’s conserved, based on the fact that the laws of physics don’t themselves change over time. But you’re asking the right kind of question.)

  As simple an idea as we can imagine—there is a quantity that doesn’t change, it stays the same as time passes. But conservation of energy and other quantities isn’t just a gentle, unintimidating place from which to launch a survey of all of physics. It’s logically the right place, since an understanding of conservation was the first step in the transition from pre-modern to modern science.

  FROM NATURES TO PATTERNS

  Put yourself in the mindset of humans trying to understand the world before physics in its modern form came along. The Greek philosopher Aristotle is usually chosen as an exemplar, though other ancient thinkers would have thought similarly. To greatly simplify a complex and subtle set of ideas, Aristotle separated the way things move into “natural” and “unnatural” (or “violent”) motions. He thought of the world as fundamentally teleological—oriented toward a future goal. Objects have natural places to be or conditions to be in, and they tend to move to those places. A rock will fall to the ground and sit there; fire will rise to the heavens.

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  Identity & Reality

  • Emile Meyerson(Author)
  • 2013(Publication Date)
  • Routledge

    (Publisher)

  Chapter V The Conservation of Energy

  THE most general formula for this principle can be stated in these terms: in every modification of an isolated system the total energy of the system conserves an invariable value.(1 ) If no account is taken of the condition of isolation, whose importance we shall see later, this formula resembles that of the conservation of matter. There is this difference that the concept of matter, which originates from common sense, is vast and without precision whereas that of energy, created ad hoc by science, seems to present all the desired precision. We shall see, however, in a later chapter that this is not absolutely so.

  Energy is ordinarily defined as the capacity of producing an effect or of accomplishing work, to use Duhem’s terms, from whom we have borrowed the formula of the principle. We shall stop provisionally at this definition, which is really applicable only to a particular form of energy (pp. 209, 218), but has certain advantages, amongst others the advantage of having great historical value, since it is in conformity with the conception of Leibniz, whose influence on the development of this chapter of physics was decisive. “Absolute force” (we know that this term for a long time designated what we call energy), says Leibniz in his Essay de Dynamique, “must be estimated according to the violent effect which it can produce.”(2 ) A projectile moving with a certain velocity can, if it strikes an obstacle, produce a determined effect: we say that it possesses a certain energy. But this same cannon-ball, placed at a certain height above the earth, will be able, in falling, to act in an analogous way. We have the right therefore, from the point of view of consequences, to assimilate these two very different concepts, motion and position, and to form the concept of energy of position, as we have just formed the concept of energy of motion or kinetic energy. The energy of position is more commonly qualified as potential

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  Foundations of Mechanical Engineering

  • A. D. Johnson(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  Newton’s laws, impulse and momentum 3

  3.1 Aims

  • To explain the interrelationship between motion, mass, inertia and forces according to the rules set out in Newton’s laws.
  • To define the equations which can be used to apply Newton’s laws to both linear and angular motion.
  • To introduce and define impulse and momentum, in both linear and angular terms.
  • To introduce and explain the principle of conservation of momentum.
  • To introduce a method of analysis by which problems relating to Newton’s Laws may be solved.

  3.2 Newton’s Laws

  Sir Isaac Newton first laid the foundations for what is known as Newtonian mechanics, by observing how masses can be manipulated by applied forces. The rules he developed are known as Newton’s laws and define the interactions between masses, forces, velocity and acceleration and have already been briefly mentioned in Chapter 1 .

  Newton also realized that all masses possess the ‘quality of inertia’, which requires forces to be used to move a mass from rest, or stop it, or reduce its velocity. Inertia cannot be felt, as can mass; however, it always accompanies mass and its effect is to oppose any force which attempts to change the state of mass.

  The effects of inertia are fundamental to Newton’s laws, both in linear and angular forms. However, it is in consideration of the angular forms of Newton’s laws that inertia is used as a calculated, finite quantity to describe the distribution of mass about an axis. For example, a bicycle wheel will possess a larger value of inertia than the same mass concentrated in a small diameter rotor. This is because most of the mass of the bicycle wheel is placed at the outer rim. It is true to say that the larger the radius at which the mass is ‘placed’, the greater the value of inertia.

  3.2.1 Newton’s first Saw

  A body will remain at rest or continue with a uniform velocity in a straight line, unless acted upon by an external force.

  Fig. 3.1

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  The Newman Lectures on Transport Phenomena

  • John Newman, Vincent Battaglia, John Newman, Vincent Battaglia(Authors)
  • 2020(Publication Date)
  • Jenny Stanford Publishing

    (Publisher)

  These concepts provide the basis for the analysis of heat transfer in solids. They also illustrate a general problem. In the study of transport processes, we find a constant interplay of Conservation Laws and transport laws, such as the first law of thermodynamics and the Fourier law of heat conduction. We want to investigate in some detail the correct formulation of these laws for fluid mechanics, heat transfer, and mass transfer.

   

  Fluid mechanics	Heat transfer	Mass transfer
  Conservation law	F = ma (also conservation of mass)	First law of thermodynamics	Conservation of mass (by species)
  Transport law

  By way of a historical survey, we might note that:

  1. In 1755, Euler wrote a differential form of the momentum balance for fluids, but he neglected viscous forces.

  2. In 1822, Navier obtained the Navier–Stokes equation.

  3. Fourier’s law of heat conduction was stated by Biot (1804, 1816) and later by Fourier [1822 (1811)].

  4. In 1855, Fick expressed a mass flux in terms of a concentration gradient.

  Progress since this time has consisted of making the macroscopic theory more coherent, of giving the macroscopic theory a microscopic basis by means of statistical mechanics, of obtaining theoretical and experimental information about transport properties, of obtaining solutions to the equations for simple transport problems, and of empirical studies of more complicated systems.

  The above comments should suggest the intimate connection of these studies with other fields of physical science, such as thermodynamics, chemical kinetics, and statistical mechanics.

  Passage contains an image

  Chapter 2 Fluid Mechanics

       

  The principal result of this chapter is the basic equations of fluid mechanics:

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  The Philosophy of Physics

  • Dean Rickles(Author)
  • 2016(Publication Date)
  • Polity

    (Publisher)

  more robust than most other such claims about the natural world. They say things about the world that are very hard to imagine not being true. In other words, they are as close to universal (empirical) truths as one can get in physical theories. Such principles are really ‘meta-laws’ (laws about laws). Special relativity, for example, involves two core principles:

  SR1 All inertial frames are equal (from the point of view of mechanical and electromagnetic physical quantities and laws). SR2 The speed of light is constant (in any and all inertial frames). Or we have the single principle of Galilean relativity satisfied by non-relativistic laws: G The laws of motion have the same form in all inertial frames (from the point of view of mechanical physical quantities and laws). In the case of thermodynamics, one has: T The laws should not allow the creation of perpetual motion machines.

  These laws govern laws: if a theory is to describe specially relativistic systems then it must contain only laws that satisfy the two principles, SR1 and SR2, above. In a sense, the principles constitute what it is to be a specially relativistic (or Galilean relativistic or thermodynamic, and so on) system. While the ‘normal’ laws of a theory might involve a reference to some specific type of system (particular particles or fields, for example), these meta-laws float above such details: they are far more general, and therefore also more robust (i.e. to changes in the specific details of the theories that implement the principles). For example, special relativity was devised before quantum mechanics came about, yet it applies just as well in quantum mechanics as it does in classical physics.

  Often, as seen above, these principles and laws concern the extent to which the reference frame, from which observations are made, is arbitrary. A reference frame can simply be understood to be a set of coordinates (x, y, z), which we can think of as a spatial frame in which measurements will be ‘recorded,’ and a time coordinate t

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